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Journal articles on the topic 'Time Dependent Diffusivity (TDD)'

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Author: Grafiati

Published: 6 September 2023

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1

Bhattacharyya, Rakhi, Banibrata Mukhopadhyay, and Malay Bandyopadhyay. "Diffusive instability in a prey-predator system with time-dependent diffusivity." International Journal of Mathematics and Mathematical Sciences 2003, no. 66 (2003): 4195–203. http://dx.doi.org/10.1155/s0161171203207274.

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An ecological model for prey-predator planktonic species has been considered, in which the growth of prey has been assumed to follow a Holling type II function. The model consists of two reaction-diffusion equations and we extend it to time-varying diffusivity for plankton population. A comparative study of local stability in case of constant diffusivity and time varying diffusivity has been performed. It has been found that the system would be more stable with time varying diffusivity depending upon the values of system parameter.

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2

Efremov, G., and T. Kudra. "Model-Based Estimate for Time-Dependent Apparent Diffusivity." Drying Technology 23, no. 12 (December 2005): 2513–22. http://dx.doi.org/10.1080/07373930500340387.

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3

Hirose, A., and O. Ishihara. "On plasma diffusion in strong turbulence." Canadian Journal of Physics 77, no. 10 (February 15, 2000): 829–33. http://dx.doi.org/10.1139/p99-069.

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It is shown that the velocity diffusivity of electrons in strong Langmuir turbulence is linearly proportional to the root-mean-square (rms) value of the electric field. The time-dependent diffusivity previously identified is a transient phenomenon. In 2-D spatial diffusion due to ExB velocity turbulence, time-dependent intermediate diffusivity emerges also followed by a well-behaved diffusivity proportional to the rms amplitude of the turbulent field.PACS Nos.: 52.25Fi, 52.35Ra, 52.65Cc

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4

Inglezakis, Vassilis J., Marco Balsamo, and Fabio Montagnaro. "A Fractal-Based Correlation for Time-Dependent Surface Diffusivity in Porous Adsorbents." Processes 8, no. 6 (June 12, 2020): 689. http://dx.doi.org/10.3390/pr8060689.

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Fluid–solid adsorption processes are mostly governed by the adsorbate transport in the solid phase and surface diffusion is often the limiting step of the overall process in microporous materials such as zeolites. This work starts from a concise review of concepts and models for surface transport and variable surface diffusivity. It emerges that the phenomenon of hindered surface diffusion for monolayer adsorption, which is common in zeolites, and models able to fit a non-monotonic trend of surface diffusivity against adsorbate solid phase concentration, have received limited attention. This work contributes to the literature of hindered diffusion by formulating a time-dependent equation for surface diffusivity based on fractal dynamics concepts. The proposed equation takes into account the contributions of both fractal-like diffusion (a time-decreasing term) and hopping diffusion (a time-increasing term). The equation is discussed and numerically analyzed to testify its ability to reproduce the possible different patterns of surface diffusivity vs. time.

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5

Kim, Min Seong, and Sean Seungwon Lee. "Design Study of Steel Fibre Reinforced Concrete Shaft Lining for Swelling Ground in Toronto, Canada." Applied Sciences 11, no. 8 (April 13, 2021): 3490. http://dx.doi.org/10.3390/app11083490.

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Reinforced concrete (RC) is a widely used construction material around the world. RC has many advantages in terms of structural stability. However, the reinforcement of RC requires extensive labour costs. Steel fibre reinforced concrete (SFRC) has been widely studied to replace steel bars in concrete structures over the decades. However, most underground structures, such as tunnel lining, are usually designed using conventional RC for long-term stability due to unexpected geotechnical characteristics, such as directional and depth-dependent varied lateral pressure, earthquakes, groundwater, and time-dependent swelling behaviour. In this paper, an alternative design of shaft structure using SFRC, based on the original RC designed data in the Toronto region, was studied to evaluate the feasibility of SFRC replacing conventional RC. A key geological feature of the site is that the bedrock is comprised of Georgian Bay shale, which exhibits long-term time-dependent deformation (TDD). The capacities of RC and SFRC for the shaft lining were calculated based on the Canadian concrete design codes CSA A23.3 and RILEM TC 162-TDF, to assess the benefit of adding steel fibre, and several analytical solutions were used to calculate the applied load on the lining. A specialised TDD constitutive model in Fast Lagrangian Analysis of Continua (FLAC) 2D was developed to estimate whether the optimum installation time of the shaft lining, based on the geological reports, is appropriate under swelling behaviour, and evaluate the resultant long-term stability. The calculated hoop thrust and bending moment for several loading cases were within the capacity of the SFRC shaft lining. The numerical analysis demonstrated that the proposed lining installation time could be reduced, despite consideration of the long-term TDD behaviour.

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6

Lesnic, D., S. A. Yousefi, and M. Ivanchov. "Determination of a time-dependent diffusivity from nonlocal conditions." Journal of Applied Mathematics and Computing 41, no. 1-2 (October 13, 2012): 301–20. http://dx.doi.org/10.1007/s12190-012-0606-4.

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7

Smyshlyaev, Andrey, and Miroslav Krstic. "On control design for PDEs with space-dependent diffusivity or time-dependent reactivity." Automatica 41, no. 9 (September 2005): 1601–8. http://dx.doi.org/10.1016/j.automatica.2005.04.006.

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8

Tirabassi, Tiziano, Marco Túllio Vilhena, Daniela Buske, and Gervásio Annes Degrazia. "An Analytical Air Pollution Model with Time Dependent Eddy Diffusivity." Journal of Environmental Protection 04, no. 08 (2013): 16–23. http://dx.doi.org/10.4236/jep.2013.48a1003.

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9

Zhang, Yurong, Huaxia Zhuang, Jiale Shi, Jun Huang, and Junzhi Zhang. "Time-dependent characteristic and similarity of chloride diffusivity in concrete." Magazine of Concrete Research 70, no. 3 (February 2018): 129–37. http://dx.doi.org/10.1680/jmacr.17.00101.

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10

Ellis, K. A., and R. A. Buhrman. "Time-dependent diffusivity of boron in silicon oxide and oxynitride." Applied Physics Letters 74, no. 7 (February 15, 1999): 967–69. http://dx.doi.org/10.1063/1.123425.

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11

Ikari, Hiroshi. "Time-Dependent Specific Heat in Vitreous Silica Using Diffusivity Measurement." Japanese Journal of Applied Physics 32, Part 1, No. 5B (May 30, 1993): 2220–22. http://dx.doi.org/10.1143/jjap.32.2220.

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12

Golestanian, R., and A. Ajdari. "Tracer diffusivity in a time- or space-dependent temperature field." Europhysics Letters (EPL) 59, no. 6 (September 2002): 800–806. http://dx.doi.org/10.1209/epl/i2002-00113-x.

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13

Vasić, Miloš, and Zagorka Radojević. "Drying Simulation of Shrinkable Clay Tiles Using Variable Diffusivity Model." Advanced Materials Research 837 (November 2013): 506–10. http://dx.doi.org/10.4028/www.scientific.net/amr.837.506.

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This paper represents the upgrade of our previous study in which we have presented a model for simulation of the drying kinetic and estimation of the effective moisture diffusivity of clay tiles using a constant diffusivity model. The main objective of this study is to determine the time - dependent effective moisture diffusivity of shrinkable clay tiles. Experimental investigations were carried out, on clay tiles, in a laboratory recirculation dryer in which drying parameters (humidity, temperature, and velocity) could be programmed, controlled and monitored during drying. Results presented in this study have shown that the proposed drying model describes and correlates accurately drying kinetics and gives a reliably estimation of the time - dependent effective moisture diffusivity.

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14

Saenko, Oleg A. "The Effect of Localized Mixing on the Ocean Circulation and Time-Dependent Climate Change." Journal of Physical Oceanography 36, no. 1 (January 1, 2006): 140–60. http://dx.doi.org/10.1175/jpo2839.1.

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Abstract Observations indicate that intense mixing in the ocean is localized above complex topography and near the boundaries. Model experiments presented here illustrate that accounting for this fact can be important. In particular, it is found that in the case of localized mixing, the rate of overturning circulation is proportional to the net rate of generation of potential energy by the vertical mixing, linked to the net downward heat diffusion, rather than to the value of the mean vertical diffusivity coefficient. Furthermore, it is shown that two climate models, having the same vertical profile of diffusivity but differing in their distribution (horizontally uniform versus topography/boundary intensified) can simulate significantly different meridional oceanic circulations, vertical heat transfers, and responses of simulated climate to atmospheric CO2 increase. This is found for relatively large [O(1.0 cm2 s−1)] horizontal-mean values of vertical diffusivity in the pycnocline. However, in cases of relatively small [O(0.1 cm2 s−1)] mean diffusivity in the pycnocline, the simulated integral quantities such as meridional mass and heat transports do not depend much on the details of the mixing distribution. Even so, it is found that the deep western boundary currents are more localized near the boundaries in the case of topography/boundary-intensified mixing; also, the stratification in the deep ocean is set through the localized regions of intense vertical mixing. In addition, it is shown that reconciling the observed basin-mean values of diffusivity in the abyssal ocean of O(10 cm2 s−1) with realistic stratification can be problematic, unless the regions of enhanced vertical mixing are localized.

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15

Wang, Hai-Long, Jian-Guo Dai, Xiao-Yan Sun, and Xiao-Long Zhang. "Time-Dependent and Stress-Dependent Chloride Diffusivity of Concrete Subjected to Sustained Compressive Loading." Journal of Materials in Civil Engineering 28, no. 8 (August 2016): 04016059. http://dx.doi.org/10.1061/(asce)mt.1943-5533.0001578.

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16

Van Bockstal, K., and M. Slodička. "Determination of a time-dependent diffusivity in a nonlinear parabolic problem." Inverse Problems in Science and Engineering 23, no. 2 (April 10, 2014): 307–30. http://dx.doi.org/10.1080/17415977.2014.900615.

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17

Vedel, Søren, and Henrik Bruus. "Transient Taylor–Aris dispersion for time-dependent flows in straight channels." Journal of Fluid Mechanics 691 (December 2, 2011): 95–122. http://dx.doi.org/10.1017/jfm.2011.444.

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AbstractTaylor–Aris dispersion, the shear-induced enhancement of solute diffusion in the flow direction of the solvent, has been studied intensely in the past half century for the case of steady flow and single-frequency pulsating flows. Here, combining Aris’s method of moments with Dirac’s bra–ket formalism, we derive an expression for the effective solute diffusivity valid for transient Taylor–Aris dispersion in any given time-dependent, multi-frequency solvent flow through straight channels. Our theory shows that the solute dispersion may be greatly enhanced by the time-dependent parts of the flow, and it explicitly reveals how the dispersion coefficient depends on the external driving frequencies of the velocity field and the internal relaxation rates for mass and momentum diffusion. Although applicable to any type of fluid, we restrict the examples of our theory to Newtonian fluids, for which we both recover the known results for steady and single-frequency pulsating flows, and find new, richer structure of the dispersion as function of system parameters in multi-frequency systems. We show that the effective diffusivity is enhanced significantly by those parts of the time-dependent velocity field that have frequencies smaller than the fluid momentum diffusion rate and the solute diffusion rate.

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18

Gama, R. P. S. da, J. R. Cerqueira, and R. M. S. da Gama. "A NOTE ON TRANSIENT HEAT TRANSFER PROBLEMS WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY AND THERMAL DIFFUSIVITY." Revista de Engenharia Térmica 19, no. 1 (September 9, 2020): 90. http://dx.doi.org/10.5380/reterm.v19i1.76439.

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In this work it is presented a numerical procedure for solving transient heat transfer problems in which the thermal diffusivity is strongly dependent on the temperature, with the aid of the Kirchhoff transformation associated to an usual finite difference approach. The first step consists of eliminating the nonlinear terms associated to the derivatives with respect to the position, by means of a Kirchhoff transformation, giving rise to a partial differential equation with only one nonlinear term (involving the coefficient of the derivative with respect to the time). The advance in time is carried out assuming the thermal diffusivity evaluated at a known temperature, giving rise to a semi-implicit scheme. Comparisons between this approach and the usual hypothesis are carried out in order to illustrate the effect of the dependence between the temperature and the thermal diffusivity. Some typical results are presented, based on the (6H-SiC) Silicon Carbide properties.

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19

Li, You Yun, Zi Quan Xiang, and Song Wang. "Identifying Time-Dependent Drug Diffusion Parameters in the Cylindrical Tube by Optimal Algorithm." Advanced Materials Research 236-238 (May 2011): 2118–21. http://dx.doi.org/10.4028/www.scientific.net/amr.236-238.2118.

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First, a FD scheme based on a polar-coordinate diffusion optimization problem is derived. Next, an optimization algorithm to compute the partial derivatives is proposed. Third, the procedure for the time-dependent drug diffusion parameters is given. Finally, the numerical result shows the validity of the optimal method based on FD to extract the effective time-dependent drug diffusivity.

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20

Fernandez, Joseph R. "Determining the Directionally-Dependent Effective Hydrogen Diffusivity of High Strength Steel Strand." Journal of Materials Science Research 5, no. 2 (January 11, 2016): 11. http://dx.doi.org/10.5539/jmsr.v5n2p11.

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<p class="1Body">An important factor in the Hydrogen Embrittlement (HE) of cold-worked carbon steel strand is the effective hydrogen diffusivity of the strand material. The speed at which HE can occur is determined by the transport of the hydrogen to locations of stress concentrations. A Scanning Kelvin Probe (SKP) was used to measure the flattened surface of strand wires before and after being charged with hydrogen to determine a relationship between the delta work function measured (and indirectly the potential of the specimen) and the presence of hydrogen near the surface of that area of the specimen. Numerous scans were performed to determine a change in delta work function between the probe and the specimen. This change in delta work function was related to the presence of hydrogen at the specimen surface over time, giving a rate of hydrogen movement within a specific area of the specimen (both in the radial and drawn directions). The change in delta work function over time was then related to the diffusion of hydrogen over time in a given area resulting in a directional effective diffusivity of hydrogen through the strand which includes the effects of hydrogen trapping and method of hydrogen transport.</p><p class="1Body">The results indicate that the effective or apparent hydrogen diffusivity in the drawn direction in pearlitic, cold worked, carbon steel strand is 5.24E-08 cm<sup>2</sup>/sec. The effective hydrogen diffusivity in the radial direction was faster (3.56E-07 cm<sup>2</sup>/sec) as compared to the wire drawn direction.</p>

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21

Fernandez, Joseph R. "Determining the Directionally-Dependent Effective Hydrogen Diffusivity of High Strength Steel Strand." Journal of Materials Science Research 5, no. 2 (January 11, 2016): 17. http://dx.doi.org/10.5539/jmsr.v5n2p17.

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<p class="1Body">An important factor in the Hydrogen Embrittlement (HE) of cold-worked carbon steel strand is the effective hydrogen diffusivity of the strand material. The speed at which HE can occur is determined by the transport of the hydrogen to locations of stress concentrations. A Scanning Kelvin Probe (SKP) was used to measure the flattened surface of strand wires before and after being charged with hydrogen to determine a relationship between the delta work function measured (and indirectly the potential of the specimen) and the presence of hydrogen near the surface of that area of the specimen. Numerous scans were performed to determine a change in delta work function between the probe and the specimen. This change in delta work function was related to the presence of hydrogen at the specimen surface over time, giving a rate of hydrogen movement within a specific area of the specimen (both in the radial and drawn directions). The change in delta work function over time was then related to the diffusion of hydrogen over time in a given area resulting in a directional effective diffusivity of hydrogen through the strand which includes the effects of hydrogen trapping and method of hydrogen transport.</p><p class="1Body">The results indicate that the effective or apparent hydrogen diffusivity in the drawn direction in pearlitic, cold worked, carbon steel strand is 5.24E-08 cm<sup>2</sup>/sec. The effective hydrogen diffusivity in the radial direction was faster (3.56E-07 cm<sup>2</sup>/sec) as compared to the wire drawn direction.</p>

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22

Guerrini, Ivan A., and D. Swartzendruber. "Soil Water Diffusivity as Explicitly Dependent on Both Time and Water Content." Soil Science Society of America Journal 56, no. 2 (March 1992): 335–40. http://dx.doi.org/10.2136/sssaj1992.03615995005600020001x.

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23

Efremov, German, Marek Markowski, Ireneusz Białobrzewski, and Magdalena Zielinska. "Approach to calculation time-dependent moisture diffusivity for thin layered biological materials." International Communications in Heat and Mass Transfer 35, no. 9 (November 2008): 1069–72. http://dx.doi.org/10.1016/j.icheatmasstransfer.2008.07.007.

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24

Nec, Yana. "Dynamics of pulse solutions in Gierer–Meinhardt model with time dependent diffusivity." Journal of Mathematical Analysis and Applications 457, no. 1 (January 2018): 585–615. http://dx.doi.org/10.1016/j.jmaa.2017.08.027.

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25

Qiu, Pengxiang, Rui Hu, Linwei Hu, Quan Liu, Yixuan Xing, Huichen Yang, Junjie Qi, and Thomas Ptak. "A Numerical Study on Travel Time Based Hydraulic Tomography Using the SIRT Algorithm with Cimmino Iteration." Water 11, no. 5 (April 30, 2019): 909. http://dx.doi.org/10.3390/w11050909.

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Travel time based hydraulic tomography is a technique for reconstructing the spatial distribution of aquifer hydraulic properties (e.g., hydraulic diffusivity). Simultaneous Iterative Reconstruction Technique (SIRT) is a widely used algorithm for travel time related inversions. Due to the drawbacks of SIRT implementation in practice, a modified SIRT with Cimmino iteration (SIRT-Cimmino) is proposed in this study. The incremental correction is adjusted, and an iteration-dependent relaxation parameter is introduced. These two modifications enable an appropriate speed of convergence, and the stability of the inversion process. Furthermore, a new result selection rule is suggested to determine the optimal iteration step and its corresponding result. SIRT-Cimmino and SIRT are implemented and verified by using two numerical aquifer models with different predefined (“true”) diffusivity distributions, where high diffusivity zones are embedded in a homogenous low diffusivity field. Visual comparison of the reconstructions shows that the reconstruction based on SIRT-Cimmino demonstrates the aquifer’s hydraulic features better than the conventional SIRT algorithm. Root mean square errors and correlation coefficients are also used to quantitatively evaluate the performance of the inversion. The reconstructions based on SIRT-Cimmino are found to preserve the connectivity of the high diffusivity zones and to provide a higher structural similarity to the “true” distribution.

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26

Richardson, W. D., F. F. Schoeggl, S. D. Taylor, B. Maini, and H. W. Yarranton. "Diffusivity of Gas Into Bitumen: Part II—Data Set and Correlation." SPE Journal 24, no. 04 (May 9, 2019): 1667–80. http://dx.doi.org/10.2118/195575-pa.

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Summary The oil-production rate of in-situ heavy-oil-recovery processes involving the injection of gaseous hydrocarbons partly depends on the diffusivity of the gas in the bitumen. Data for gas diffusivities, particularly above ambient temperature, are relatively scarce because they are time consuming to measure. In this study, the diffusion and solubilities of gaseous methane, ethane, propane, and n-butane in a Western Canadian bitumen were measured from 40 to 90°C and pressures from 300 to 2300 kPa, using a pressure-decay method. The diffusivities were determined from a numerical model of the experiments that accounted for the swelling of the oil. In Part I of this study (Richardson et al. 2019), it was found that both constant and viscosity-dependent diffusivities could be used to model the mass of gas diffused and the gas-concentration profile in the bitumen; however, the constant diffusivity was different for each experiment and mainly depended on the oil viscosity. In this study, a correlation for the constant diffusivity to the oil viscosity is developed as a tool to quickly estimate the gas diffusivity. A correlation of diffusivity to the mixture viscosity is also developed for use in more-rigorous diffusion models. The maximum deviations in the mass diffused over time predicted with the constant and viscosity-dependent (mixture viscosity) correlations at each condition are on average 7.4 and 8.7%, respectively.

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27

Karabelchtchikova, Olga, and Richard D. Sisson. "Calculation of Gas Carburizing Kinetics from Carbon Concentration Profiles based on Direct Flux Integration." Defect and Diffusion Forum 266 (September 2007): 171–80. http://dx.doi.org/10.4028/www.scientific.net/ddf.266.171.

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Initiated by the need of industry for gas carburizing process control and optimization, this paper focuses on understanding the effect of the time, temperature and carbon potential on the mass transfer coefficient and carbon diffusivity in Austenite. A method for direct flux integration has previously been proposed to calculate these kinetic parameters from the experimental carbon concentration profiles. AISI 8620 steel discs were gas carburized at different levels of atmosphere carburizing potential for selected austenizing temperatures. Analyses of the carburized parts included experimental measurement of weight gain, surface carbon concentration and carbon concentration profiles. The time-dependent weight gain and surface carbon content measurements allowed calculation of the time average mass transfer coefficient, while carbon concentration profiles were used to calculate the concentration dependent carbon diffusivity for selected process parameters. Excellent agreement was found between the calculated mass transfer coefficient and carbon diffusivity values and those reported in the literature. The calculated values served as input in the previously developed carburizing model validating the predicted results by comparison with the experimental concentration profiles.

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28

Saheb, Nouari, and Umer Hayat. "Temperature-dependent thermal properties of spark plasma sintered alumina." Science of Sintering 49, no. 2 (2017): 117–28. http://dx.doi.org/10.2298/sos1702117s.

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In this work, we report temperature-dependent thermal properties of alumina powder and bulk alumina consolidated by spark plasma sintering method. The properties were measured between room temperature and 250?C using a thermal constants analyzer. Alumina powder had very low thermal properties due to the presence of large pores and absence of bonding between its particles. Fully dense alumina with a relative density of 99.6 % was obtained at a sintering temperature of 1400?C and a holding time of 10 min. Thermal properties were found to mainly dependent on density. Thermal conductivity, thermal diffusivity, and specific heat of the fully dense alumina were 34.44 W/mK, 7.62 mm2s-1, and 1.22 J/gK, respectively, at room temperature. Thermal conductivity and thermal diffusivity decreased while specific heat increased with the increase in temperature from room temperature to 250?C.

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29

Haddar, Houssem, Jing-Rebecca Li, and Simona Schiavi. "A Macroscopic Model for the Diffusion MRI Signal Accounting for Time-Dependent Diffusivity." SIAM Journal on Applied Mathematics 76, no. 3 (January 2016): 930–49. http://dx.doi.org/10.1137/15m1019398.

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30

Barbu, Viorel, and Gabriela Marinoschi. "Existence for a time-dependent rainfall infiltration model with a blowing up diffusivity." Nonlinear Analysis: Real World Applications 5, no. 2 (April 2004): 231–45. http://dx.doi.org/10.1016/s1468-1218(03)00033-6.

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31

Hussein, M. S., and D. Lesnic. "Determination of a time-dependent thermal diffusivity and free boundary in heat conduction." International Communications in Heat and Mass Transfer 53 (April 2014): 154–63. http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.02.027.

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32

Duine, Peter A., Jilt Sietsma, A. van den Beukel, and Arjen M. Vredenberg. "Time-dependent diffusivity of Au in amorphous Pd40Ni40P20 measured by Rutherford-backscattering spectrometry." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 71, no. 4 (September 1992): 445–50. http://dx.doi.org/10.1016/0168-583x(92)95363-v.

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33

Le Minh, Triet, Phong Luu Hong, and Quan Pham Hoang. "An asymmetric backward problem for the inhomogeneous parabolic equation with time-dependent diffusivity." Computational and Applied Mathematics 37, no. 3 (September 9, 2017): 3241–55. http://dx.doi.org/10.1007/s40314-017-0509-y.

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34

Shchekin, Alexander K., Anatoly E. Kuchma, and Elena V. Aksenova. "The Effects of Viscosity and Capillarity on Nonequilibrium Distribution of Gas Bubbles in Swelling Liquid–Gas Solution." Colloids and Interfaces 7, no. 2 (May 5, 2023): 39. http://dx.doi.org/10.3390/colloids7020039.

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A detailed statistical description of the evolution of supersaturated-by-gas solution at degassing has been presented on the basis of finding the time-dependent distribution in radii of overcritical gas bubbles. The influence of solution viscosity and capillarity via internal pressure in the bubbles on this distribution has been considered until the moment when the gas supersaturation drops due to depletion and stops nucleation of new overcritical gas bubbles. This study aims to find the nonstationary growth rate of overcritical bubbles depending on gas supersaturation, diffusivity and solubility in solution, solution viscosity, and surface tension on bubble surface. Other important factors are linked with the initial rate of homogeneous gas bubble nucleation and coupling between diffusivity and viscosity in the solution. Here, we numerically studied how all these factors affect the time-dependent distribution function of overcritical bubbles in their radii, maximal and mean bubble radii, and the time-dependent swelling ratio of a supersaturated-by-gas solution in a wide range of solution viscosities.

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35

Singh, Rohit R., Ashok S. Sangani, Susan Daniel, and Donald L. Koch. "The combined hydrodynamic and thermodynamic effects of immobilized proteins on the diffusion of mobile transmembrane proteins." Journal of Fluid Mechanics 877 (August 27, 2019): 648–81. http://dx.doi.org/10.1017/jfm.2019.592.

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The plasma membranes of cells are thin viscous sheets in which some transmembrane proteins have two-dimensional mobility and some are immobilized. Previous studies have shown that immobile proteins retard the short-time diffusivity of mobile particles through hydrodynamic interactions and that steric effects of immobile proteins reduce the long-time diffusivity in a model that neglects hydrodynamic interactions. We present a rigorous derivation of the long-time diffusivity of a single mobile protein interacting hydrodynamically and thermodynamically with an array of immobile proteins subject to periodic boundary conditions. This method is based on a finite element method (FEM) solution of the probability density of the mobile protein diffusing with a position-dependent mobility determined through a multipole solution of Stokes equations. The simulated long-time diffusivity in square arrays decreases as the spacing in the array approaches the particle size in a manner consistent with a lubrication analysis. In random arrays, steric effects lead to a percolation threshold volume fraction above which long-time diffusion is arrested. The FEM/multipole approach is used to compute the long-time diffusivity far away from this threshold. An approximate analysis of mobile protein diffusion through a network of pores connected by bonds with resistances determined by the FEM/multipole calculations is then used to explore higher immobile area fractions and to evaluate the finite simulation cell size scaling behaviour of diffusion near the percolation threshold. Surprisingly, the ratio of the long-time diffusivity to the spatially averaged short-time diffusivity in these two-dimensional fixed arrays is higher in the presence of hydrodynamic interactions than in their absence. Finally, the implications of this work are discussed, including the possibility of using the methods developed here to investigate more complex diffusive phenomena observed in cell membranes.

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36

Zhao, Xuewei, Xiaoxiao Wei, Hongwei Wang, Xingli Liu, Yanyan Zhang, and Hua Zhang. "Discrepancy of Effective Water Diffusivities Determined from Dynamic Vapor Sorption Measurements with Different Relative Humidity Step Sizes: Observations from Cereal Materials." Foods 12, no. 7 (March 30, 2023): 1470. http://dx.doi.org/10.3390/foods12071470.

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Water diffusivity, a critical parameter for cereal processing design and quality optimization, is usually concentration-dependent. dynamic vapor sorption (DVS) system provides an approach to establishing the relationship between water concentration and diffusivity. However, the usual relative humidity (RH) jump during practical sorption processes is usually greater than that adopted in DVS measurements. Water vapor sorption kinetics of glutinous rice grains, glutinous rice flour and wheat flour dough films were measured using the DVS system to verify if varying RH step sizes can obtain identical diffusivities within the same range. The effective diffusivities were determined according to Fick’s second law. The results revealed that increasing RH step size led to a higher estimated diffusivity, regardless of whether the water concentration gradient or potential chemical gradient was considered a driving force for water diffusion. This finding was further confirmed by a linear RH scanning DVS measurement. The water concentration-dependent diffusivity obtained from a multi-step DVS measurement, according to Fick’s second law, will overestimate the required time for practical cereal drying or adsorption. Thus, this paradoxical discrepancy needs a new mass transfer mechanism to be explained.

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Ji, Ying, and K. O. Homan. "On Simplified Models for the Rate- and Time-Dependent Performance of Stratified Thermal Storage." Journal of Energy Resources Technology 129, no. 3 (February 15, 2007): 214–22. http://dx.doi.org/10.1115/1.2748814.

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In direct sensible thermal storage systems, both the energy discharging and charging processes are inherently time-dependent as well as rate-dependent. Simplified models which depict the characteristics of this transient process are therefore crucial to the sizing and rating of the storage devices. In this paper, existing models which represent three distinct classes of models for thermal storage behavior are recast into a common formulation and used to predict the variations of discharge volume fraction, thermal mixing factor, and entropy generation. For each of the models considered, the parametric dependence of key performance measures is shown to be expressible in terms of a Peclet number and a Froude number or temperature difference ratio. The thermal mixing factor for each of the models is reasonably well described by a power law fit with Fr2Pe for the convection-dominated portion of the operating range. For the uniform and nonuniform diffusivity models examined, there is shown to be a Peclet number which maximizes the discharge volume fraction. In addition, the cumulative entropy generation from the simplified models is compared with the ideally-stratified and the fully-mixed limits. Of the models considered, only the nonuniform diffusivity model exhibits an optimal Peclet number at which the cumulative entropy generation is minimized. For each of the other models examined, the cumulative entropy generation varies monotonically with Peclet number.

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Strauß, Florian, Thomas Geue, Jochen Stahn, and Harald Schmidt. "Neutron Reflectometry for the Investigation of Self-Diffusion in Amorphous Silicon." Defect and Diffusion Forum 363 (May 2015): 225–30. http://dx.doi.org/10.4028/www.scientific.net/ddf.363.225.

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We present experiments based on neutron reflectometry in combination with 29Si/natSi isotope multilayers in order to investigate the self-diffusion in amorphous silicon. Such experiments allow the detection of diffusion processes in the amorphous state on length scales below 10 nm. First results at 650 °C show a continuous decrease of the artificial Bragg peak produced by the multilayer, corresponding to a diffusivity of (1.1 ± 0.4) x 10-20 m2/s on a length scale of 2 - 7 nm. The diffusivity is not time-dependent for annealing times between 3 min and 1 h. Compared to recent measurements in silicon single crystals by the same method, the diffusivity is higher by a factor of about 105.

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Broadbridge, Philip, and Joanna M. Goard. "Conditionally Integrable Nonlinear Diffusion with Diffusivity 1/u." Symmetry 11, no. 6 (June 18, 2019): 804. http://dx.doi.org/10.3390/sym11060804.

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An explicit mapping is given from the space of general complex meromorphic functions to a space of special time-dependent solutions of the 1 + 2-dimensional nonlinear diffusion equation with diffusivity depending on concentration as D = 1 / u. These solutions have constant-flux boundary conditions. Some simple examples are constructed, including that of a line source enclosed by a cylindrical barrier. This has direct application to electron diffusion in a laser-heated plasma.

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Luan, Tran Nhat, and Tra Quoc Khanh. "Determination of Initial Distribution for a Space-Fractional Diffusion Equation with Time-Dependent Diffusivity." Bulletin of the Malaysian Mathematical Sciences Society 44, no. 5 (April 24, 2021): 3461–87. http://dx.doi.org/10.1007/s40840-021-01118-7.

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Nguyen, Khieu-Van, Denis Le Bihan, Luisa Ciobanu, and Jing-Rebecca Li. "The time-dependent diffusivity in the abdominal ganglion of Aplysia californica: experiments and simulations." Biomedical Physics & Engineering Express 5, no. 4 (July 23, 2019): 045036. http://dx.doi.org/10.1088/2057-1976/ab301e.

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Liu, Chein-Shan. "A two-stage Lie-group shooting method (TSLGSM) to identify time-dependent thermal diffusivity." International Journal of Heat and Mass Transfer 53, no. 21-22 (October 2010): 4876–84. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.06.005.

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43

Schulz, Robert, Kenji Yamamoto, André Klossek, Roman Flesch, Stefan Hönzke, Fiorenza Rancan, Annika Vogt, et al. "Data-based modeling of drug penetration relates human skin barrier function to the interplay of diffusivity and free-energy profiles." Proceedings of the National Academy of Sciences 114, no. 14 (March 20, 2017): 3631–36. http://dx.doi.org/10.1073/pnas.1620636114.

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Based on experimental concentration depth profiles of the antiinflammatory drug dexamethasone in human skin, we model the time-dependent drug penetration by the 1D general diffusion equation that accounts for spatial variations in the diffusivity and free energy. For this, we numerically invert the diffusion equation and thereby obtain the diffusivity and the free-energy profiles of the drug as a function of skin depth without further model assumptions. As the only input, drug concentration profiles derived from X-ray microscopy at three consecutive times are used. For dexamethasone, skin barrier function is shown to rely on the combination of a substantially reduced drug diffusivity in the stratum corneum (the outermost epidermal layer), dominant at short times, and a pronounced free-energy barrier at the transition from the epidermis to the dermis underneath, which determines the drug distribution in the long-time limit. Our modeling approach, which is generally applicable to all kinds of barriers and diffusors, allows us to disentangle diffusivity from free-energetic effects. Thereby we can predict short-time drug penetration, where experimental measurements are not feasible, as well as long-time permeation, where ex vivo samples deteriorate, and thus span the entire timescales of biological barrier functioning.

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Vasić, Miloš, and Zagorka Radojević. "Drying Kinetic Simulation of Clay Tiles Made from the Raw Material Having Less Clay Fraction." Advanced Materials Research 1036 (October 2014): 3–8. http://dx.doi.org/10.4028/www.scientific.net/amr.1036.3.

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In order to describe the internal moisture rate and to take all different mechanisms of moisture movement into account, it is suitable to use effective diffusivity as a measure of moisture rate, irrespectively of the mechanisms really involved. This means that all different mechanisms and driving forces for internal moisture transport are lumped together and introduced into effective moisture diffusivity. Hence, diffusion equations are retained and reused with the effective diffusivity coefficient as a measuring parameter of internal moisture ratio. In our previous studies we have presented the calculation method which assumed constant diffusivity. The next goal was to estimate effective diffusivity at various moisture contents, in a real case of non-linear drying curves, and to predict drying kinetic. In our last study we have developed a model for determination of the variable effective diffusivity and identification of the exact transition points between possible drying mechanisms. In this paper we have tried to develop more accurate tool for determination of time dependent effective moisture diffusivity. An analytical model and computing procedure were developed to evaluate mass transfer properties and describe drying kinetic of clay tiles having less clay fraction. The proposed procedure was validated with experimental drying data. Presented results have demonstrated that the proposed dying model can be applied for the accurate description of experimental drying kinetics and a reliable estimation of effective diffusivity.

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Hobiny, Aatef, and Ibrahim Abbas. "Generalized Thermo-Diffusion Interaction in an Elastic Medium under Temperature Dependent Diffusivity and Thermal Conductivity." Mathematics 10, no. 15 (August 4, 2022): 2773. http://dx.doi.org/10.3390/math10152773.

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The purpose of this work is to investigate, within the context of extended thermo-diffusion theory, the transient thermo-diffusion responses for a half-space with variable thermal conductivity and diffusivity. The half-bounding space’s surface is traction-free and exposed to a time-dependent thermal shock, but the chemical potential is believed to be a known function of time. Because the nonlinear equations are complicated, the finite element technique is applied to solve these equations. Numerical outcomes are produced and graphically illustrated. The effects of varying thermal conductivity and diffusivity on the response are studied using parameter studies. Using the results of this study, researchers hope to understand better how thermo-mechanical fields interact in real materials. By ignoring the new parameter, a comparison of numerical results and analytical cases is produced, and the behavior of physical quantities for numerical solutions is studied to ensure that the proposed technique is accurate.

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Leaist, Derek G. "Moments analysis of restricted ternary diffusion: sodium sulfite + sodium hydroxide + water." Canadian Journal of Chemistry 63, no. 11 (November 1, 1985): 2933–39. http://dx.doi.org/10.1139/v85-486.

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Ternary diffusion coefficients can be determined from restricted-diffusion experiments by evaluating zeroth and first time moments of the difference in a concentration-dependent property measured at two levels along the diffusion column. The method is used to determine ternary diffusion coefficients for aqueous sodium sulfite + sodium hydroxide solutions from conductance measurements. It is shown that these data can be analyzed to obtain the ternary diffusivity of sulfur dioxide in strongly alkaline solutions where sulfite is the major transporting species for the sulfur dioxide component. At high pH values, coupled flow of hydroxide ions leads to a significant increase in the diffusivity of the sulfur dioxide component relative to its diffusivity in pure water. Binary diffusion coefficients for aqueous sodium sulfite solutions are also reported.

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Mi, Changwen, Kaikai Shao, and Xiaobao Li. "On the Durability of Sealable Circular Concrete Structures under Chloride Environment." Advances in Materials Science and Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/510845.

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Reinforcement corrosion resulting from chloride attack is one major mechanism that compromises concrete durability. Numerical methods were commonly used for tackling Fick’s diffusion equations. In this paper, we developed a Crank-Nicolson based finite difference scheme suitable for circular concrete structures. Both a time-dependent surface chloride model and diffusivity were considered. The impact of an ideal sealer on chloride redistribution was further investigated. Results suggested that the chloride threshold depth in a concrete structure is greatly affected by the radius of curvature, environment severity, and diffusivity. For sealable concrete structures, both the sealer application timing and location are of great importance.

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Cherstvy, Andrey G., and Ralf Metzler. "Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity." Journal of Statistical Mechanics: Theory and Experiment 2015, no. 5 (May 15, 2015): P05010. http://dx.doi.org/10.1088/1742-5468/2015/05/p05010.

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Lin, Xijian, Qi Pan, and Yan He. "In situ detection of protein corona on single particle by rotational diffusivity." Nanoscale 11, no. 39 (2019): 18367–74. http://dx.doi.org/10.1039/c9nr06072c.

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The volume-dependent rotational diffusion coefficient of gold nanorod was used to monitor the formation of protein corona in homogeneous solution in real time. The detection of particle thickness change could reach subnanometer sensitivity.

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Sánchez-Ramírez, J. F., J. L. Jiménez Pérez, A. Cruz Orea, R. Gutierrez Fuentes, A. Bautista-Hernández, and U. Pal. "Thermal Diffusivity of Nanofluids Containing Au/Pd Bimetallic Nanoparticles of Different Compositions." Journal of Nanoscience and Nanotechnology 6, no. 3 (March 1, 2006): 685–90. http://dx.doi.org/10.1166/jnn.2006.124.

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Colloidal suspensions of bimetallic Au/Pd nanoparticles were prepared by simultaneous reduction of the metal ions from their corresponding chloride salts with polymer (PVP) stabilizer. Thermal properties of water containing bimetallic nanoparticles with different nominal compositions (Au/Pd = 12/1, 5/1, 1/1, 1/5) were measured using the mode mismatched dual-beam thermal lens technique to determine the effect of particle composition on the thermal diffusivity of the nanofluids. The characteristic time constant of the transient thermal lens was estimated by fitting the experimental data to the theoretical expression for transient thermal lens. The thermal diffusivity of the nanofluids (water, containing Au/Pd bimetallic nanoparticles) is seen to be strongly dependent on the composition of the particles. The maximum diffusivity was achieved for the nanoparticles with highest Au/Pd molar ratio. A possible mechanism for such high thermal diffusivity of the nanofluids with bimetallic particles is given. UV-Vis spectroscopy, TEM and high-resolution electron microscopy (HREM) techniques were used to characterize the Au/Pd bimetallic nanoparticles.

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